We have a two party system because we have no viable 3rd parties. It's not like there are dozens of 3rd parties clawing around 10% of the vote. You can add up all of the 3rd parties in the past election and they don't add up to 10% of the vote. They may not add up to 5% of the vote. Proportional representation doesn't change any of that. You would still have 3rd parties gathering 2-3% of the vote total. That's not statistically significant enough to warrant any sort of representation.
I have no idea what good would come from splitting the executive office. You could potentially have two executives from two different parties. That doesn't seem like it would improve things.
I don't think term limits would make things any worse. Many states have term limits at the local, city and county levels. They seem to survive just fine.